數(shù)字信號處理a雙語chapter6ztransa140404

1、上講回顧上講回顧lz變換的定義：變換的定義：lz變換和變換和dtft的關(guān)系：的關(guān)系：lz平面和收斂域平面和收斂域nnzngzg)( )() jjj nz eng zg eg n e z 變換收斂域的特點：變換收斂域的特點：l收斂域是一個圓環(huán)，有時可向內(nèi)收縮到原點收斂域是一個圓環(huán)，有時可向內(nèi)收縮到原點有時可向外擴(kuò)展到有時可向外擴(kuò)展到，只有序列，只有序列(n)的收斂域的收斂域是整個是整個z平面平面l收斂域內(nèi)無極點，收斂域內(nèi)無極點，x(z)在收斂域內(nèi)每一點上在收斂域內(nèi)每一點上都是解析函數(shù)。都是解析函數(shù)。lz 變換表示法：級數(shù)形式、解析表達(dá)式變換表示法：級數(shù)形式、解析表達(dá)式 （注意（注意:函數(shù)收斂域，

2、缺一不可）函數(shù)收斂域，缺一不可）chapter 6z-transformchapter 6 z-transformlpart a: z-transformlpart b: the inverse z-transform and z-transform theoremslpart c: convolution(卷積卷積) lpart d: the transfer functionlintroductionl6.1 definitionl6.2 rational z-transforms(有理有理z變換變換)l6.3 region of convergence（收斂域）（收斂域） of a ra

3、tional z-transform part a: z-transformpart a: introductionlthe dtft provides a frequency-domain (頻域頻域) representation of discrete-time signals and lti（線（線性時不變）性時不變）discrete-time systems.lbecause of the convergence condition, in many cases, the dtft of a sequence may not exist.las a result, it is not

4、 possible to make use of such frequency-domain characterization in these cases.part a: introductionlin general, zt can be thought of as a generalization of the dtft. zt is more complex than dtft (both literally and figuratively), but provides a great deal of insight into system design and behavior.

5、lfor discrete-time systems, zt plays the same role of laplace-transform does in continuous time systems. zt characterizes signals or lti systems in complex frequency domain（復(fù)頻域）（復(fù)頻域）.6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6

6、.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transformimzjrez0平面zaz a6.1 definition of z-transform imzjrez0平面zaz a6.1 defin

7、ition of z-transformtable 6.1 some commonly used z-transform pairslintroductionl6.1 definitionl6.2 rational z-transforms(有理有理z變換變換)l6.3 region of convergence（收斂域）（收斂域） of a rational z-transform part a: z-transform6.2 rational z-transform6.2 rational z-transform6.2 rational z-transform6.2 rational z-

8、transform6.2 rational z-transform6.2 rational z-transform6.2 rational z-transform6.2 rational z-transforml零極點共軛成對出現(xiàn)、收斂域內(nèi)無極點零極點共軛成對出現(xiàn)、收斂域內(nèi)無極點l需注意的是：求解零、極點時，為避免遺漏，需注意的是：求解零、極點時，為避免遺漏，需需先將先將z變換有理分式的分子和分母都轉(zhuǎn)換成變換有理分式的分子和分母都轉(zhuǎn)換成z的正數(shù)次冪的正數(shù)次冪，再進(jìn)行求解，詳見第，再進(jìn)行求解，詳見第26頁頁ppt。11()1x zaz zza lintroductionl6.1 definiti

9、onl6.2 rational z-transforms(有理有理z變換變換)l6.3 region of convergence（收斂域）（收斂域） of a rational z-transform part a: z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence

10、of a rational z-transform6.3 region of convergence of a rational z-transform有限長序列的有限長序列的z變換變換有限長序列的有限長序列的z變換變換例例1：序列：序列x（n）=（n）的）的z變換變換 由于由于n1=n2=0，其收斂域為整個閉域，其收斂域為整個閉域 z平面，平面，0|z|0( )( )11nnx zn zz 例例2：矩形序列：矩形序列x（n）=rn（n） 有限項等比級數(shù)求和有限項等比級數(shù)求和 112(1)0( )( )11nnnnnnnx zrn zzzzz 11( ), 0|1nzxzzz 0(1)1naq

11、q 6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transformz變換的收斂域包括變換的收斂域包括 點是因果序列的特征。點是因果序列的特征。6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 r

12、egion of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transformwherellllllaaabbbaaabbbaaabbbsos2102102212022212021211012111012211